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# Find the sum to infinity of the series 1/2 , 1/6, 1/18, .....

### Question

Find the sum to infinity of the series 1/2 , 1/6, 1/18, .....

### Options

A) 2/3

B) 1/3

C) 3/4

D) 1

$$a=\frac{1}{2}\\r=\frac{\frac{1}{6}}{\frac{1}{2}}=\frac{1}{6}\times\frac{2}{1}=\frac{1}{3}\\S_n = \frac{a}{1-r}\\S_n = \frac{\frac{1}{2}}{1-\frac{1}{3}}\\=\frac{\frac{1}{2}}{\frac{3}{2}}\\=\frac{1}{2}\times\frac{3}{2}\\=\frac{3}{4}$$
• $$a=\frac{1}{2}\\r=\frac{\frac{1}{6}}{\frac{1}{2}}=\frac{1}{6}\times\frac{2}{1}=\frac{1}{3}\\S_n = \frac{a}{1-r}\\S_n = \frac{\frac{1}{2}}{1-\frac{1}{3}}\\=\frac{\frac{1}{2}}{\frac{3}{2}}\\=\frac{1}{2}\times\frac{3}{2}\\=\frac{3}{4}$$